To answer this question IMO, yes. When EA bought Westwood, they wanted they want to go in a different direction of universes and they stay separate, and that's how the C&C series went downhill, even after C&C3.

Quite interesting to read Zee Hypnotist's rare post there.

Hi there, used to be a prominent member in the C&C community (whatever that means), visited the studios quite a few times and met a lot of the developers.First of all, please forgive any mistakes in my memory, some of the information I'm posting here is recollected from as far back as 2007 or 2008.The answer to your question is yes and no.Red Alert 1 was originally meant to be a spinoff, nothing more. It was supposed to be a joke, with appearances by Kane to entertain the player, and that was it. Think of it like a glorified version of Kane's dino funpark, except it's an entirely new game.Westwood, however, was not expecting the enormous praise that Red Alert 1 got. They were happy people liked it, but they didn't expect to need an expansion, or two, for that matter. They thought at the time it would be a silly one-game spinoff that would be a fun project, nothing more.With the success of Red Alert 1, they decided to intend to tie Red Alert to the Tiberium series. Kane's appearance fit perfectly. There were plans for games such as Renegade 2 that would tie Red Alert 2 to Renegade 1 / Tiberian Dawn, but unfortunately, Renegade 2 was cancelled.When EA took over, they decided to push the series in a different direction, keeping the games distinct and separate. EA eventually announced that Red Alert and Tiberian themes would be separate. However, you can see hints of connection. For example:

Phase tank in Aftermath obviously acts like the Stealth Tank in the Tiberian games. The Mirage Tank is supposed to be somewhat similar, in that it is a tank that changes it's appearance.

Soviets have tesla technology, which is, interestingly enough, similar to the powerful defense that the Scrin have in C&C 3, which Kane may or may not have been aware of.

Ultimately, the remaining Westwood staff at Petroglyph in 2008 explained their take on the C&C series, hinting at how they would have moved it, but ultimately, they made it clear that EA was the new franchise owner, and ultimately, former Westwood staff plain couldn't talk about it, due to legal issues.Here's an archived link of a Q and A session that they participated in. It doesn't really delve into the link between Tiberium and Red Alert too much, but it's an interesting thread nonetheless.